{"id":"https://openalex.org/W2012985567","doi":"https://doi.org/10.1142/s0218127403006522","title":"THE SAME DISTRIBUTION OF LIMIT CYCLES IN FIVE PERTURBED CUBIC HAMILTONIAN SYSTEMS","display_name":"THE SAME DISTRIBUTION OF LIMIT CYCLES IN FIVE PERTURBED CUBIC HAMILTONIAN SYSTEMS","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2012985567","doi":"https://doi.org/10.1142/s0218127403006522","mag":"2012985567"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127403006522","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127403006522","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111220210","display_name":"Zhengrong Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I189210763","display_name":"Yunnan University","ror":"https://ror.org/0040axw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I189210763"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"ZHENGRONG LIU","raw_affiliation_strings":["Department of Mathematics, Yunnan University,  Institute of Applied Mathematics, Yunnan Province, Kunming,  Yunnan 650091, P.R. China","Department of Mathematics, Yunnan University, Institute of Applied Mathematics, Yunnan Province, Kunming, Yunnan 650091, P.R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yunnan University,  Institute of Applied Mathematics, Yunnan Province, Kunming,  Yunnan 650091, P.R. China","institution_ids":["https://openalex.org/I189210763"]},{"raw_affiliation_string":"Department of Mathematics, Yunnan University, Institute of Applied Mathematics, Yunnan Province, Kunming, Yunnan 650091, P.R. China","institution_ids":["https://openalex.org/I189210763"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101294483","display_name":"Zhiyan Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I189210763","display_name":"Yunnan University","ror":"https://ror.org/0040axw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I189210763"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"ZHIYAN YANG","raw_affiliation_strings":["Department of Mathematics, Yunnan University,  Institute of Applied Mathematics, Yunnan Province, Kunming,  Yunnan 650091, P.R. China","Department of Mathematics, Yunnan University, Institute of Applied Mathematics, Yunnan Province, Kunming, Yunnan 650091, P.R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yunnan University,  Institute of Applied Mathematics, Yunnan Province, Kunming,  Yunnan 650091, P.R. China","institution_ids":["https://openalex.org/I189210763"]},{"raw_affiliation_string":"Department of Mathematics, Yunnan University, Institute of Applied Mathematics, Yunnan Province, Kunming, Yunnan 650091, P.R. China","institution_ids":["https://openalex.org/I189210763"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003278204","display_name":"Tao Jiang","orcid":"https://orcid.org/0000-0002-9478-2589"},"institutions":[{"id":"https://openalex.org/I189210763","display_name":"Yunnan University","ror":"https://ror.org/0040axw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I189210763"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"TAO JIANG","raw_affiliation_strings":["Department of Mathematics, Yunnan University,  Institute of Applied Mathematics, Yunnan Province, Kunming,  Yunnan 650091, P.R. China","Department of Mathematics, Yunnan University, Institute of Applied Mathematics, Yunnan Province, Kunming, Yunnan 650091, P.R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yunnan University,  Institute of Applied Mathematics, Yunnan Province, Kunming,  Yunnan 650091, P.R. China","institution_ids":["https://openalex.org/I189210763"]},{"raw_affiliation_string":"Department of Mathematics, Yunnan University, Institute of Applied Mathematics, Yunnan Province, Kunming, Yunnan 650091, P.R. China","institution_ids":["https://openalex.org/I189210763"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5111220210"],"corresponding_institution_ids":["https://openalex.org/I189210763"],"apc_list":null,"apc_paid":null,"fwci":3.096,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.91087011,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"13","issue":"01","first_page":"243","last_page":"249"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.989799976348877,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9761999845504761,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.7912989854812622},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.7100209593772888},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6282466053962708},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.6055514216423035},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.5627059936523438},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4866805672645569},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4438640773296356},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38707271218299866},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2375151515007019},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1089121401309967}],"concepts":[{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.7912989854812622},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.7100209593772888},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6282466053962708},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6055514216423035},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.5627059936523438},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4866805672645569},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4438640773296356},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38707271218299866},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2375151515007019},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1089121401309967}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127403006522","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127403006522","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1141904788","https://openalex.org/W1984092501","https://openalex.org/W1990636372","https://openalex.org/W2040825728","https://openalex.org/W2046858619","https://openalex.org/W2061361830","https://openalex.org/W2160545686","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2051439117","https://openalex.org/W4388297534","https://openalex.org/W1673883441","https://openalex.org/W3195693990","https://openalex.org/W4298109871","https://openalex.org/W2313188567","https://openalex.org/W4248124207","https://openalex.org/W2996059826","https://openalex.org/W2083477739","https://openalex.org/W2087320822"],"abstract_inverted_index":{"Using":[0],"the":[1,15,46,62,69],"method":[2],"of":[3,18,32,48],"qualitative":[4],"analysis":[5],"we":[6,44],"show":[7],"that":[8],"five":[9,56],"perturbed":[10,57],"cubic":[11],"Hamiltonian":[12],"systems":[13,58],"have":[14,22],"same":[16],"distribution":[17,54],"limit":[19,24,34,50],"cycles":[20,25,51],"and":[21,52],"11":[23,49],"for":[26],"some":[27],"parameters.":[28],"The":[29],"accurate":[30],"location":[31],"each":[33],"cycle":[35],"is":[36],"given":[37],"by":[38],"numerical":[39],"exploration.":[40],"In":[41],"other":[42],"words,":[43],"demonstrate":[45],"existence":[47],"their":[53],"in":[55,59],"two":[60],"ways,":[61],"results":[63],"obtained":[64],"from":[65],"both":[66],"ways":[67],"are":[68],"same.":[70]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}